The Startling Story behind a Famous Footnote

Progress is a slippery word; but none can doubt that price theory, the preoccupation with markets that historically has at the heart of economics, has seen a great deal of elaboration in the least 75 years. Jerry Green, of Harvard University, gave a graphic illustration when he travelled to Middlebury Colllege last fall to give a lecture on the history of the discipline. He carried with him a series of graduate micro texts.

He held up Microeconomic Theory: A Mathematical Approach, by James Henderson and Richard Quandt, the slim book (291 pp.) with which he began his graduate education in the 1960s. H&Qhad made waves when it first appeared in 1958, Green noted. Earlier texts – The Theory of Price, by George Stigler, say, or Economic Analysis, by Kenneth Boulding — derived mainly from Alfred Marshall’s 1890 classic, Principles of Economics. These literary expositions bristled with diagrams, but there were no equations.

H&Q was just the beginning. In rapid order came Edmond Malinvaud’s Lectures in Microeconomic Theory (1972) and, in 1978, Hal Varian’s Microeconomic Analysis. In 1990 David Kreps introduced game theory and decision theory to the curriculum with A Course in Microeconomic Theory (850 pp.). The current best-seller, Microeconomic Theory, by Andreu Mas-Colell, Michael D. Whinston, and Harvard’s Green followed in 1995 (981 pp.). The first volume (584 pp) of Kreps’ magnum opus Microeconomic Foundationsappeared in 2012, dealing mainly with choice and competitive markets. Kreps promises a second volume on game theory and strategy and a third treating various advanced topics of incentives.

Understand, this is not really about textbooks at all. The growth of knowledge has produced a series of correlative jobs in the world itself, not just teaching competition and cooperation in university departments and business schools, but practicing in government offices, law firms, courts, and consultancies around the world. If it is regulated – or deregulated, unregulated, or re-regulated – it is a matter of microeconomics.

What happened? The post-war mathematization of economics stems in general from two epochal works, Foundations of Economic Analysis (1947), by Paul Samuelson, and, with a lag, The Theory of Games and Economic Behavior (1944), by John von Neumann and Oskar Morgenstern. But books are advertisements for particular programs seeking concrete results. One mathematical adventure more than any other is said to underlay the expansion of microeconomics in the second half of the twentieth century: the proof, in 1952 or ’53 or ’54, of the existence of a competitive general equilibrium.

It had been intuitively obvious since Adam Smith that, in an economic system, everything depends on everything else, and thought possible, since Leon Walras, to calculate and measure such a system – in other words, to produce a blueprint to test against the world. But proving that such a coherence is possible in the first place in a world of many competing individuals was the necessary first step to describing it in detail. And, as Mas-Colell, of Pompeu Fabra Univesity, in Barcelona, has put it, the existence proof was “the door that opens into the house of analysis”

For thirty years the official story of general equilibrium went like this: Kenneth Arrow and Gerard Debreu, working independently at first, then joining forces, proved that Adam Smith was right, and the rest is history. Beginning with Jürg Niehans’ magisterial A History of Economic Theory: Classic Contrbutions 1720-1980 (Johns Hopkins, 1990), the received version shifted slightly.

By 1950, under the influence of The Theory of Games and Economic Behavior, convexity and duality were very much on the minds of mathematical economists. Nevertheless, the only economic models for which a general equilibrium had been proved were those of Wald and von Neumann, the first for an economically unappealing model, the other for a growth model without final consumption. In Value and Capital, though it introduced English-reading economists to general equilibrium, [John] Hicks never bothered about existence proofs and negative prices. Indeed, he sometimes expressed himself as if he believed that the counting of equations and variables was enough. Morgenstern, then learning about these things from von Neumann, chided Hicks mercilessly (and unfairly) for his mathematical complacency.

It remained for Arrow, who admired Hicks, and to Debreu, to prove the existence of a competitive equilibrium for a Walrasian general equilibrium model. J. F. Nash’s existence proof for a n-person game, mentioned above in the chapter John von Neumann, showed the way. The result was the 1954 Arrow-Debreu model of general equilibrium, the neatest and most compact model of an economy since Cantillon’s [literary] Tableau Economique, in terms of land, and vastly richer and more general.*

* An existence proof of a somewhat different kind was published earlier in the same year by Lionel McKenzie).

That the footnote was there in Niehans owes to Duke University economist and historian of thought E. Roy Weintraub.

It was some time in the 1970s that Weintraub first became aware that McKenzie, by then of the University of Rochester, had in the early 1950s proved the same result as had Arrow and Debreu, and slightly earlier at that, but somehow had failed to share in the enormous credit assigned or their famous result.

Weintraub had several reasons to be interested. For one thing, he had been hired by Duke to replace McKenzie as a mathematical economist after the position had gone unfilled thirteen years. Then, too, McKenzie was a Duke alumnus. He had transferred there after two years at Middle George College and done so well that he left in 1939 with a Rhodes Scholarship.

Weintraub had a side interest in the rise of mathematical economics because it had sidelined pretty completely his father, Sidney Weintraub, a distinguished price theorist at the University of Pennsylvania, who had been born too early to catch hold of the mathematical wave.

Finally, Weintraub was in some sense a recovering mathematician himself. As a doctoral student at Penn in the mid-Sixties, he had run head-on into the graduate version of the “new math,” the program devised by a secret club of French mathematicians known to the world as the Bourbaki (after an obscure nineteenth century French general named Nicholas Bourbaki). The Bourbaki has set out to rewrite mathematics from the general to the specific. Lacking a grounding in concrete applications, Weintraub struggled (as did many others) as his professors taught structure instead of applications. Major tools went undiscussed. Weintraub has written: “Vector spaces over fields were at best a corollary, and finite vector spaces over the real numbers were simply left for problem 7, optional.” In the end, He retreated to a degree in applied math and economics. “You were a member of the lost generation,” commiserated mathematician Phillip Griffiths many years later. All this in “Bleeding Hearts to Dessicated Robots,” an autobiographical essay in How Economics Became a Mathematical Science(2002).

McKenzie, too, was a member of a lost generation. War broke out in Europe in September 1939, so McKenzie headed for Princeton University instead of Oxford. After two years of courses there the war swept him up and he spent four years in various jobs (cable censor in Panama and New York among them) that permitted him to bone up on the mathematics he had missed at Princeton. By the time he finally made it to Britain, in 1946, to take up his Rhodes, the Oxbridge universities had begun their decades-long rear-guard action against the mathematization of economics. After two years, Oxford declined to vote him an D.Phil. He returned to Duke to teach. He gave up on his Princeton PhD after his thesis adviser, trade theorist, Frank Graham, jumped off the upper deck of Palmer Stadium during a football game. It wasn’t until he visited the Cowles Commission, at the University of Chicago, in 1950, when he was 31, that McKenzie’s luck turned..

The Cowles Commission was, as Weintraub describes it “somewhere between a university department and a national laboratory.” Established in 1931 by wealthy investor Alfred Cowles with a view to investigating the causes of the Great Depression (and furthering the aims of the newly-established Econometric Society), the commission had been charged during World War II with developing a working model of the US economy. Though it shared space with the economics department of the University of Chicago, the two centers diverged widely in their temperaments and aims. Cowles was a hotbed of new-fangled mathematical economics; the department, led by Milton Friedman, was becoming the preeminent center of old-fashioned price theory. Within a few years Cowles would leave Chicago for Yale – but not before McKenzie had succeeded in rehabilitating the kernel of his derailed Princeton thesis, and, as something of an afterthought, setting out an existence proof in “On Equilibrium of World Trade in Graham’s Model of World Trade and Other Competitive Systems.” The paper appeared in Econometrica in April 1954.

Also at Cowles, at slightly different times, were Arrow and Debreu. Arrow spent two years there, 1948-50. Already, with his dissertation, he had conjured a whole new field of study, dubbed social choice, demonstrating with a powerful proof that the hope of reaching a single best way to satisfy individual preferences through voting was a pipe-dream, no matter what system was employed. Debreu arrived from Paris in 1950, deeply trained in Bourbakist mathematics and somewhat insulated from the emphasis on planning methods that dominated Cowles at the time. He and Arrow began working on the equilibrium proof separately; when learning of each other’s work, they threw their lots in together and presented their results at the 1952 meetings of the Econometric Society, in Chicago – a day after McKenzie had talked about his work. Their paper, “Existence of an Equilibrium for a Competitive Economy,” appeared in Econometrica eighteen months later, more general than that of McKenzie, but three months after his.

Not long after, McKenzie would begin one of the greatest second acts in twentieth-century economics. Unable to get a job at a top-five university (Princeton at least awarded him his Ph.D. on the basis of his journal articles), he signed on at the University of Rochester in 1957 on the strength of a promise that he could build a department. Paul Samuelson had done something of the same thing at the Massachusetts Institute of Technology, beginning fifteen years before. And so McKenzie did. He began by hiring trade theorist Ronald Jones, a prize student of Robert Solow. From modest beginnings, Rochester went on to become one of the most successful training grounds for young economists in the world, producing such notable figures as Robert Fogel, Stanley Engerman, Gary Gorton, Sherwin Rosen, Rudiger Dornbusch, Michael Mussa, Buz Brock, Hugo Sonnenschein, Jose Scheinkman, Jerry Green, Robert King, Mark Bils, Robert Barro and Paul Romer, McKenzie declined to leave when Stanford asked him to replace Arrow; for McKenzie’s reflections on the satisfactions of it, see this note, for example.

Weintraub learned all this in the late ’70s, in the course of retooling as a historian of economic thought. The result was a long review article, “The Existence of a Competitive General Equilibrium, 1930-1954,” in the Journal of Economic Literature, in 1983. McKenzie’s name was at last on its way to being firmly appended to the famous proof — small comfort, perhaps, considering the Nobel Prize that Debreu would receive in 1985 for his contributions to mathematical economics. McKenzie didn’t even make Mark Blaug’s list of “the hundred greatest economists since Keynes,” when it was published that same year.

Weintraub kept after it. He noticed that the principals had been somewhat reluctant to discuss the details surrounding their respective proofs. He badgered them, gradually learned that Debreu had attended McKenzie’s session and hadn’t told Arrow about it. The matter of priority clearly bothered McKenzie, too, not a lot, but such that he returned to it in conversations with friends. In the only autobiographical account he gave, delivered orally at Keio University, in Japan, in June 1998, on the occasion of an honorary degree, he stuck to the stoic account of his originality he had given Weintraub for his 1983 article.

By the early ’00s, Wientraub was back in the hunt. Arrow’s account of Debreu’s omission was now in the record. Much archival material had become available. Weintraub took a second stab at assessing the record, in 2002, this time in collaboration with a mathematically sophisticated student, Ted Gayer. The behind-the-scenes background of the Arrow-Debreu paper was coming clearer all the time.

Enter a young German researcher, Till Duppe, with access to the Debreu papers, maintained at the University of California at Berkeley, where Debreu had taught for thirty years. The two met via an Internet conference and agreed to collaborate. Further details had emerged, including an astonishing fact: the anonymous referee, who bottled UP McKenzie’s submission to Econometrica for a critical time, while Arrow and Debreu tidied up their proof, was none other than Debreu himself; and Debreu hadn’t disclosed his conflict of interest to the editor, Robert Solow. Debreu’s conduct was thus revealed as having been dishonorable. Imagine if Rosalind Franklin had actually described the double helical structure of the DNA molecule and James Watson and Francis Crick hadn’t bothered to cite her!

Düppe published previously undisclosed details of Debreu’s life in a remarkable biographical article in History of Political Economy – a dark Dickensian childhood, lifelong obsession with secrecy, family life shattered after he received his Nobel, eventual dementia. Weintraub published a third article, this time in the Journal of Economic Perspectives, surveying the concealed flow and ebb of tensions between Debreu and McKenzie over the years. McKenzie, who died in 2010, lived long enough to read the last draft.

All this, and a good deal more is laid out in Finding Equilibrium: Arrow, Debreu, McKenzie and the Problem of Scientific Credit, by Weintraub and Düppe, published last week by Princeton University Press. The personalities are discussed. The chronology gets quite a going-over; the indeterminacy of the dates on which the first satisfactory proof was communicated to a larger world is examined. To my mind it doesn’t change the story that much. There are all kinds of reasons the story came out the way it did. The authors examine them all.

They settle on what the great sociologist Robert K. Merton dubbed “the Matthew effect,” quoting the Gospel: “For unto everyone that hath shall be given, he shall have abundance; but from him that hath not shall be taken away even that which he hath.” Credit, in other words, flows more easily to those who are better known. The authors’ aim was to “re-personalize” mathematical economics, and they certainly have done that.